使用k-聚类大爆炸-大坍缩算法及后处理方法进行多模态优化中最优解的识别与量化
Multimodal Optimization with k-Cluster Big Bang-Big Crunch Algorithm and Postprocessing Methods for Identification and Quantification of Optima
AI总结：
本文扩展大爆炸-大坍缩算法提出k-BBBC多模态优化器，并引入两种后处理方法用于识别和量化最优解，在基本多模态函数上准确度和成功率优于其他方法，但需预知最优解数量。
摘要：
多模态优化在工程问题中经常遇到，特别是在寻找不同且可替代的解决方案时。进化算法凭借种群概念、探索/开发能力以及适合并行计算等特性，能够高效处理多模态优化。本文研究了一种鲜为人知的优化器——大爆炸-大坍缩（BBBC）算法是否适用于多模态优化。我们扩展了BBBC并提出k-BBBC，一种基于聚类的多模态优化器。此外，我们引入了两种后处理方法，用于(i)在一组检索到的解（即种群）中识别局部最优解，以及(ii)量化相对于预期最优解而言正确检索到的最优解数量（即成功率）。我们的结果表明，k-BBBC在具有大量最优解（测试了379个最优解）和高维度（测试了32个决策变量）的问题上表现良好，但对于具有许多局部最优解的问题（即在CEC'2013基准测试集中），其计算成本过高。与其他多模态优化方法相比，在基本多模态函数上测试时，它在准确度（在搜索空间和目标空间中）和成功率（正确检索到的最优解数量）方面优于它们，尤其是在应用精英主义时；然而，它需要预先知道问题的最优解数量，这使得其在小生境竞争测试CEC'2013上的性能下降。最后，我们通过将所提后处理方法的成功率与实际成功率进行比较来验证其有效性：结果表明，这些方法可用于评估多模态优化算法的性能，通过正确识别最优解并提供成功指示——而无需知道最优解在搜索空间中的具体位置。
英文摘要：
Multimodal optimization is often encountered in engineering problems, especially when different and alternative solutions are sought. Evolutionary algorithms can efficiently tackle multimodal optimization thanks to their features such as the concept of population, exploration/exploitation, and being suitable for parallel computation. This paper investigates whether a less-known optimizer, the Big Bang-Big Crunch (BBBC) algorithm, is suitable for multimodal optimization. We extended BBBC and propose k-BBBC, a clustering-based multi-modal optimizer. Additionally, we introduce two post-processing methods to (i) identify the local optima in a set of retrieved solutions (i.e., a population), and (ii) quantify the number of correctly retrieved optima against the expected ones (i.e., success rate). Our results show that k-BBBC performs well even with problems having a large number of optima (tested on $379$ optima) and high dimensionality (tested on $32$ decision variables), but it becomes computationally too expensive for problems with many local optima (i.e., in the CEC'2013 benchmark set). Compared to other multimodal optimization methods, it outperforms them in terms of accuracy (in both search and objective space) and success rate (number of correctly retrieved optima) when tested on basic multimodal functions, especially when elitism is applied; however, it requires knowing the number of optima of a problem, which makes its performance decrease when tested on niching competition test CEC'2013. Lastly, we validated our proposed post-processing methods by comparing their success rate to the actual one: results suggest that these methods can be used to evaluate the performance of a multimodal optimization algorithm by correctly identifying optima and providing an indication of success -- without the need to know where the optima are located in the search space.
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